Definition 3.3 (Spline-oriented multirate RK scheme) 

We consider a \(s\) -staged Runge–Kutta (RK) scheme [1]} given by the Butcher tableau \(\left(A,b,c\right)\) . Based on the DSF-approach, one macro step of a spline-oriented multirate RK scheme with \(m\)  micro steps, applied to (REF ), advances the solution \(\left(y_{n}^{\lbrace S\rbrace },y_{n}^{\lbrace F\rbrace }\right)\)  at \(t_n = t_0 + n \cdot H\)  to the solution \(\left(y_{n+1}^{\lbrace S\rbrace },y_{n+1}^{\lbrace F\rbrace }\right)\)  at \(t_{n+1} = t_{n} + H\)  as follows:
